Let’s see how different neighborhood matrix styles can impact the estimates of spatial regression models. Again, run the code below in order to have the data in place for this exercises.

## Reading layer `OGRGeoJSON' from data source 
##   `https://geoportal.stadt-koeln.de/arcgis/rest/services/Basiskarten/kgg/MapServer/20/query?where=objectid+is+not+null&text=&objectIds=&time=&geometry=&geometryType=esriGeometryEnvelope&inSR=&spatialRel=esriSpatialRelIntersects&distance=&units=esriSRUnit_Foot&relationParam=&outFields=*&returnGeometry=true&returnTrueCurves=false&maxAllowableOffset=&geometryPrecision=&outSR=4326&havingClause=&returnIdsOnly=false&returnCountOnly=false&orderByFields=&groupByFieldsForStatistics=&outStatistics=&returnZ=false&returnM=false&gdbVersion=&historicMoment=&returnDistinctValues=false&resultOffset=&resultRecordCount=&returnExtentOnly=false&datumTransformation=&parameterValues=&rangeValues=&quantizationParameters=&featureEncoding=esriDefault&f=geojson' 
##   using driver `GeoJSON'
## Simple feature collection with 543 features and 20 fields
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: 6.77253 ymin: 50.83045 xmax: 7.162028 ymax: 51.08496
## Geodetic CRS:  WGS 84
## ℹ Using "','" as decimal and "'.'" as grouping mark. Use `read_delim()` for more control.
## Rows: 949 Columns: 79
## ── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
## Delimiter: ";"
## chr  (3): wahl, ags, gebiet-name
## dbl (71): gebiet-nr, max-schnellmeldungen, anz-schnellmeldungen, A1, A2, A3, A, B, B1, C, D, E, F, D1, F1, D2, F2, D3, F3, D4, F4, D5, F5, D6, F6, D7,...
## lgl  (4): D30, F30, D31, F31
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## 
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voting_districts <-
  glue::glue(
    "https://geoportal.stadt-koeln.de/arcgis/rest/services/Basiskarten/kgg/\\
    MapServer/20/query?where=objectid+is+not+null&text=&objectIds=&time=&\\
    geometry=&geometryType=esriGeometryEnvelope&inSR=&spatialRel=\\
    esriSpatialRelIntersects&distance=&units=esriSRUnit_Foot&relationParam=&\\
    outFields=*&returnGeometry=true&returnTrueCurves=false&maxAllowableOffset=\\
    &geometryPrecision=&outSR=4326&havingClause=&returnIdsOnly=false&return\\
    CountOnly=false&orderByFields=&groupByFieldsForStatistics=&outStatistics=\\
    &returnZ=false&returnM=false&gdbVersion=&historicMoment=&returnDistinct\\
    Values=false&resultOffset=&resultRecordCount=&returnExtentOnly=false&datum\\
    Transformation=&parameterValues=&rangeValues=&quantizationParameters=&\\
    featureEncoding=esriDefault&f=geojson"
  ) %>% 
  sf::st_read(as_tibble = TRUE) %>%
  sf::st_transform(3035) %>% 
  dplyr::transmute(Stimmbezirk = as.numeric(nummer))

afd_votes <-
  glue::glue(
    "https://www.stadt-koeln.de/wahlen/bundestagswahl/09-2021/praesentation/\\
    Open-Data-Bundestagswahl476.csv"
  ) %>% 
  readr::read_csv2() %>%
  dplyr::transmute(Stimmbezirk = `gebiet-nr`, afd_share = (F1 / F) * 100)

election_results <-
  dplyr::left_join(
    voting_districts,
    afd_votes,
    by = "Stimmbezirk"
  )

immigrants_cologne <-
  z11::z11_get_100m_attribute(STAATSANGE_KURZ_2) %>%
  terra::crop(election_results) %>%
  terra::mask(terra::vect(election_results))


inhabitants_cologne <-
  z11::z11_get_100m_attribute(Einwohner) %>%
  terra::crop(election_results) %>%
  terra::mask(terra::vect(election_results))

immigrant_share_cologne <-
  (immigrants_cologne / inhabitants_cologne) * 100

election_results <-
  election_results %>%
  dplyr::mutate(
    immigrant_share = 
      exactextractr::exact_extract(immigrant_share_cologne, ., 'mean'),
    inhabitants = 
      exactextractr::exact_extract(inhabitants_cologne, ., 'mean')
  )

1

Re-use the code from the previous exercise for the Queen neighborhoods. But this time do one weight matrix with row-normalization and another one with minmax-normalization. Insert them into two spatial regression lag models of your choice using the same variables as in the lecture, i.e., both of them should either be a Spatial Lag Y or Spatial Lag X model.
For minmax-normalization, you would have to use the option style = "minmax" in the spdep:nb2listw() function.
# spdep
queen_neighborhood <-
  spdep::poly2nb(
    election_results,
    queen = TRUE
  )

queen_W <- spdep::nb2listw(queen_neighborhood, style = "W")

queen_minmax <- spdep::nb2listw(queen_neighborhood, style = "minmax")

# run regressions
spatial_lag_y_W <-
  spatialreg::lagsarlm(
    afd_share ~ immigrant_share + inhabitants,
    data = election_results,
    listw = queen_W
    )

spatial_lag_y_minmax <-
  spatialreg::lagsarlm(
    afd_share ~ immigrant_share + inhabitants,
    data = election_results,
    listw = queen_minmax
    )

2

Calculate the impacts of both models. What is your observation?
spatialreg::impacts(spatial_lag_y_W, listw = queen_W)
## Impact measures (lag, exact):
##                      Direct    Indirect       Total
## immigrant_share -0.05999312 -0.09788693 -0.15788005
## inhabitants     -0.03747085 -0.06113877 -0.09860962
spatialreg::impacts(spatial_lag_y_minmax, listw = rook_W)
## Impact measures (lag, exact):
##                      Direct    Indirect      Total
## immigrant_share -0.11174858 -0.08429008 -0.1960387
## inhabitants     -0.06714851 -0.05064900 -0.1177975
# There are some slight differences in the estimate of the indirect effects but
# more severe one in the calculation of the direct ones.